# Opportunity Cost

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University of Toronto Scarborough

Economics for Management Studies

MGEA02H3

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Summer

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OPPORTUNITY COST AND PPC
Knowledge Summary:
1. Opportunity of something is the value of the next best alternative given up, in other words, it
is the value that was sacrificed in order to obtain that thing.
2. Opportunity cost has two parts Explicit cost and implicit cost
3. E.g., opportunity cost of consuming burger
Instead of consuming burger, we can consume coke.
The cost of buying the burger is the explicit cost
The joy we give up from consuming coke is the implicit cost.
4. The key for opportunity cost is the production possibilities Frontier
5. The PPF expresses the combination of X and Y that we can consume for a given amount of
resources.
6. The slope of the tangent line to each point on the PPF is the opportunity cost of X
7. The formulas required is:
Opportunity cost of X = -dy/dx - Units of Y we have to give up if we want a little bit of X
Opportunity cost of Y = -dx/dy - Units of X we have to give up if we want a little bit of Y Summary of Questions to be asked
1. Opportunity cost calculation
o Obtain the PPF function
o Derive the first derivative the PPF
F’(x) = dy/dx
o Substitute the value of X to calculate the opportunity cost of X
F’(y) = dx/dy = 1/(dy/dx)
o Thus, 1/the opportunity cost of X = opportunity cost of Y
2. X or Y to be consumed to maximize total utility for a given utility function
o Obtain the utility function U = F1(X,Y)
o Obtain the PPF Y = F2(X)
o Substitute Y = F2(X) to utility function
o Thus, the total utility function only have U = F(X)
o Derive the first derivative of the total utility function in the above step f’(x) = dU/dx
o Set the first derivative to be zero and solve the X dU/dX = 0
o The value calculated in the above step is the value of X that can maximize total utility
Related Exam Questions
Questions from 2011 Midterm
Question 1-3
Answers
1) The opportunity cost of Y is -dX/dY or -1/(dY/dX). Y = 8(400 – X ) . dY/dX = 8*0.5(400-
X ) -0(-2X) . -dY/dX = 8X(400-X ) 2 -0.. When X = 12, the opportunity cost of X = 6, so the
opportunity cost of Y = 1/6. The correct answer is (D).
2 -0.5
2) From above, the opportunity cost of X is 8X(400-X ) . When X = 16, the opportunity cost of
X = 10.6667 or 10 ⅔. The correct answer is (H).
2 2 0.5 2 2 2
3) U

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